Answer:
a+c=199...equation 1
8.5 a+5 c=1,366...equation 2
The number of adults tickets sold=106
The number of children tickets sold=93
Explanation:
a). Determine first expression
Let the number of each group be as follows;
adults=a
children=c
total number of people=199
This can be expressed as;
number of people=number of children+number of adults
replacing;
a+c=199...equation 1
b). Determine the second expression
Let the total amount made by the opening night can be expressed as shown;
total amount=(price per child ticket×number of children)+(price per adult ticket×number of adults)
where;
total amount=$1,366
price per child ticket=$5
number of children=c
cost per adult=$8.5
number of adults=a
replacing;
(8.5×a)+(5×c)=1,366
8.5 a+5 c=1,366...equation 2
c). Combine equation 1 and 2 and solve simultaneously
1(8.5 a+5 c=1,366)
-
5(a+c=199)=5 a+5 c=995
(8.5 a-5 a)+(5 c-5 c)=(1,366-995)
3.5 a=371
a=371/3.5
a=106
replacing the value for a in equation 1
106+c=199
c=199-106=93
The number of adults tickets sold=106
The number of children tickets sold=93